Japan's Nikkei index closed up 1%, and Hong Kong's Hang Seng closed up 2.7%.
The Nikkei index soon climbed 3.6%, capturing nearly half of the previous day's losses.
Japan's Nikkei index closed at 8, 429.45 on Friday - its lowest year-end close since 1982.
Elsewhere in Asia, Japan's benchmark Nikkei index slipped as the yen gained ground against the dollar.
Japan may be a basket case, but the Nikkei Index is trading at its book value!
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The Nikkei index, at 10344 yesterday, is basically flat to the 10546 at the end of 2009.
But its markets took a tumble this week, with the Nikkei index losing 4.1% on Tuesday alone.
Today, March 12, the Nikkei index registered its first decline in nine days, falling 34 points to 12, 314 yen.
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In Asia, the fall was led by Japan's Nikkei index, which closed down 7.3% having fallen as much as 10%.
On Wednesday, the benchmark Nikkei index rose 2.3% to 15, 096, with carmaker Toyota and electronics giant Sony leading the gains.
Japanese shares were higher on Mr Kuroda's comments with the Nikkei index hitting a new high for 2013 in early trading.
As reflected by the precipitous slide in the Nikkei Index, Japanese stocks have been out of favor for more than two decades.
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The Nikkei index ended the week with Friday trading up nearly 3%.
If the Nikkei index were to slip back below the 15, 000 level which it hit late last year, another wave of banking failures would ensue.
Last week the Nikkei Index shot up 8% in one day when the Japanese government "accepted" the state of affairs and closed down Hokkaido Takushoku Bank.
Since the beginning of the year, the market has seen a 50% rise in the Nikkei index, helped by a fall in the value of the yen.
At the time of this posting (late Sunday night, central time) the Nikkei index was down more than 6% and shares of Tokyo Electric were off 24%.
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Stocks fell nevertheless directly after the news, with the Nikkei index registering an almost 2% decline, and futures indicating another 3 % decline for a total 5% fall.
After being closed Friday for a holiday, the Nikkei index in Tokyo fell 2.8% on concerns about European debt and Friday's weaker-than-expected jobs report in the United States.
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Another poor performer was Tokyo's Nikkei index, which closed with a 27.2% loss on the year - and a massive 34% drop from the highs reached in March.
You also lost a great deal of money if you purchased Japanese stocks in the late 1980s and sold them recently the Japanese Nikkei Index (NYSE:EWJ) is down 80 percent.
Analysts said that given the sharp rise, some investors had been keen to book profits over the past few days, which has also contributed to the recent decline in the Nikkei index.
Asian shares had earlier closed lower, with the situation in the eurozone being closely monitored around the world, with Japan's Nikkei index and Hong Kong's Hang Seng both falling 1.4%.
Shares in Asia also closed down sharply, with Japan's main Nikkei index suffering its biggest one-day drop since the 1987 stock market crash and Hong Kong's Hang Seng slumping to a three-year low.
Yet between now and close of business on March 31st, the government will be doing its best to rig the country's stockmarket so that the Nikkei index ends the financial year above 18, 000.
The Japanese Nikkei Index is down 70 percent.
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News that a brash internet company, livedoor, was under investigation for market manipulation and accounting irregularities (see article) had sparked two days of widespread selling during which the benchmark Nikkei index and the broader Topix both fell by 5.7%.
Japan's Nikkei 225 index lost 2.2 percent to 13, 475.64, echoing U.S. stock markets losses Friday.
Japan's Nikkei 225 index shed its morning gains and was down 0.3 percent to 14, 246.07.
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